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arXiv:2204.10643

Quantum Proof of Work with Parametrized Quantum Circuits

Mikhail Y. Shalaginov, Michael Dubrovsky

Published Apr 22, 2022• 4 citations
arXivHTMLPDF

Abstract

Despite all the progress in quantum technologies over the last decade, there is still a dearth of practical applications for quantum computers with a small number of noisy qubits. The effort to show quantum supremacy has been largely focused on demonstrating computations that cannot be accomplished on a classical computer at all, a difficult and controversial target. Quantum advantage (a speedup over classical computers) is a more practical milestone for today's modest quantum processors. In this work, we proposed a scheme for quantum-computer compatible proof of work (cryptographic mechanism used in Bitcoin mining) and verified it on a 4-qubit superconducting quantum node.

DOI
10.48550/arxiv.2204.10643

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Despite all the progress in quantum technologies over the last decade, there is still a dearth of practical applications for quantum computers with a small number of noisy qubits. The effort to show quantum supremacy has been largely focused on demonstrating computations that cannot be accomplished on a classical computer at all, a difficult and controversial target. Quantum advantage (a speedup over classical computers) is a more practical milestone for today's modest quantum processors. In this work, we proposed a scheme for quantum-computer compatible proof of work (cryptographic mechanism used in Bitcoin mining) and verified it on a 4-qubit superconducting quantum node.
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Quantum computational advantage was claimed for the first time in 2019 and several experiments since then have reinforced and strengthened the claim. At the same time, a new generation of quantum computing devices with 100 logical qubits is being built. This raises two questions: Has quantum advantage actually been achieved? And what should our next milestones be for the upcoming 100-logical-qubit era? In this perspective, I argue that, in fact, quantum advantage has been achieved. The status today is analogous to Bell-inequality violations in the 1980s where some loopholes remain open, specifically, scalability and verifiability. I then outline three milestones for the 100-logical-qubit era aiming to close those loopholes: demonstrate fault-tolerant quantum advantage, perform efficiently verifiable advantage using random circuits with symmetries, and eventually demonstrate classically verifiable advantage with applications to certified randomness. These milestones are also natural stepping stones towards running algorithms with cryptographic applications.
Proof-of-Work (PoW) is a fundamental underlying technology behind most major blockchain cryptocurrencies. It has been previously pointed out that quantum devices provide a computational advantage in performing PoW in the context of Bitcoin. Here we make the case that this quantum advantage extends not only to all existing PoW mechanisms, but to any possible PoW as well. This has strong consequences regarding both quantum-based attacks on the integrity of the entirety of the blockchain, as well as more legitimate uses of quantum computation for the purpose of mining Bitcoin and other cryptocurrencies. For the first case, we estimate when these quantum attacks will become feasible, for various cryptocurrencies, and discuss the impact of such attacks. For the latter, we derive a precise formula to calculate the economic incentive for switching to quantum-based cryptocurrency miners. Using this formula, we analyze several test scenarios, and conclude that investing in quantum hardware for cryptocurrency mining has the potential to pay off immensely.
The key cryptographic protocols used to secure the internet and financial transactions of today are all susceptible to attack by the development of a sufficiently large quantum computer. One particular area at risk is cryptocurrencies, a market currently worth over 100 billion USD. We investigate the risk posed to Bitcoin, and other cryptocurrencies, by attacks using quantum computers. We find that the proof-of-work used by Bitcoin is relatively resistant to substantial speedup by quantum computers in the next 10 years, mainly because specialized ASIC miners are extremely fast compared to the estimated clock speed of near-term quantum computers. On the other hand, the elliptic curve signature scheme used by Bitcoin is much more at risk, and could be completely broken by a quantum computer as early as 2027, by the most optimistic estimates. We analyze an alternative proof-of-work called Momentum, based on finding collisions in a hash function, that is even more resistant to speedup by a quantum computer. We also review the available post-quantum signature schemes to see which one would best meet the security and efficiency requirements of blockchain applications.
The last five years have seen a dramatic evolution of platforms for quantum computing, taking the field from physics experiments to quantum hardware and software engineering. Nevertheless, despite this progress of quantum processors, the field is still in the noisy intermediate-scale quantum (NISQ) regime, seriously limiting the performance of software applications. Key issues involve how to achieve quantum advantage in useful applications for quantum optimization and materials science, connected to the concept of quantum supremacy first demonstrated by Google in 2019. In this article we will describe recent work to establish relevant benchmarks for quantum supremacy and quantum advantage, present recent work on applications of variational quantum algorithms for optimization and electronic structure determination, discuss how to achieve practical quantum advantage, and finally outline current work and ideas about how to scale up to competitive quantum systems.